Question: The grades on a chemistry midterm at Springer are normally distributed with $\mu = 75$ and $\sigma = 4.0$. William earned a n $87$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{87 - {75}}{{4.0}}} $ ${ z \approx 3.00}$ The z-score is $3.00$. In other words, William's score was $3.00$ standard deviations above the mean.